Small area estimation with stochastic benchmark constraints : teory and practical application in US labor statistics

The Bureau of Labor Statistics uses state-space time series models to produce small area labor force estimates from the monthly Current Population Survey (CPS). For each area, a separate model is fitted that combines a classical components model for the unobservable population values with a model for the sampling errors. The use of the model produces estimators with much smaller variances than the survey estimates, but the models can be slow to adapt to external shocks to the economy if they occur towards the end of the series. To protect the area models from this type of bias, we constrain each month the model estimates to add up to the aggregate direct CPS estimate in a set of areas for which the latter is sufficiently accurate. This is done by combining individual area models into a multivariate state-space model and adding the benchmark constraints to the joint observation equation. Because the CPS design involves partial replacements of sample units each month, the survey errors are autocorrelated. The conventional approach to handling autocorrelated survey errors requires a very high order state-space system with large computational demands. We develop new algorithms for handling autocorrelated measurement errors with a lower order system. These algorithms produce concurrent and historical estimates that satisfy the benchmarks, along with their variances. Our approach differs from conventional benchmarking. First, model dependent estimates are often benchmarked to external data that is only recorded at few time points, resulting in retrospective benchmarking with potentially large revisions to the published data. In our approach benchmarking takes place concurrently so that the estimates adapt to external shocks as they occur. Second, we use benchmarks that are not independent of the input data for the models (the sum of the area estimates in the present application). The empirical illustrations use CPS series, to illustrate benchmarking during 2001 when the U.S. economy experienced major shocks. We describe the estimating approach used in the United States for developing official labor force estimates for States and large areas. Actual estimating issues associated with this approach and which led to the decision to conduct research on concurrent benchmarking are discussed. Empirical illustrations include the development of official labor force estimates for 2001 using the interim benchmarking approach implemented by BLS with official labor force estimates for January 2005.